Question

The following three defense stocks are to be combined into a stock index in January 2016 (perhaps a portfolio manager believes these stocks are an appropriate benchmark for his or her performance):

		Price
	Shares (millions)		1/1/16			1/1/17			1/1/18
Douglas McDonnell	215		$	64		$	68		$	82
Dynamics General	455			72			64			78
International Rockwell	250			101			90			106

a. Calculate the initial value of the index if a price-weighting scheme is used.

b. What is the rate of return on this index for the year ending December 31, 2016? For the year ending December 31, 2017? (A negative value should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

Answer 1

(a)-Initial Value of the index if a price-weighting scheme is used

Initial Value of the index = Average of the Price on 1/1/16

= [$64 + $72 + $101] / 3

= $237 / 3

= $79

“Initial Index = $79.00”

(b)- Rate of return on this index for the year ending December 31, 2016 & for the year ending December 31, 2017

Rate of return on this index for the year ending December 31, 2017

Average Index Value on 01/01/2016 = $79

Average Index Value on 01/01/2017 = $74 [($68 + $64 + $90) / 3]

Therefore, the Rate of Return = [(Average Index Value on 01/01/2017 - Average Index Value on 01/01/2016) / Average Index Value on 01/01/2016] x 100

= [($74 - $79) / $74] x 100

= [-$5 / $79] x 100

= -6.33% (Negative)

Rate of return on this index for the year ending December 31, 2017

Average Index Value on 01/01/2017 = $74

Average Index Value on 01/01/2018 = $88.67 [($82 + $78 + $106) / 3]

Therefore, the Rate of Return = [(Average Index Value on 01/01/2018 - Average Index Value on 01/01/2017) / Average Index Value on 01/01/2017] x 100

= [($88.67 - $74) / $74] x 100

= [$14.67 / $74] x 100

= 19.82%

FINAL ANSWER

Rate of return on this index for the year ending December 31, 2016 = -6.33% (Negative)

Rate of return on this index for the year ending December 31, 2017 = 19.82%